Structured light from helical undulators

Shunya Matsuba

Hiroshima synchrotron radiation center Hiroshima University

The 9th Asian Forum for Accelerators and Detectors

2018/0131

1

Introduction

• Structured light means light which have spatially controlled intensity, polarization and (or) phase distribution.

• Spatially uniform polarization state with left-handed or right-handed spiral phase front called optical vortex.

2

Optical vortex

3

equiphasic surface equiphasic surfacePhase condition on a vertical plane

Normal beam Optical Vortex

Phase condition on a vertical plane

Laguerre-Gauss mode

L𝐺𝑝𝑙 𝑟, 𝜙 =2𝑝!

𝜋 𝑝+ 𝑙 !

1

𝑤 𝑧

𝑟 2

𝑤 𝑧

𝑙

exp−𝑟2

𝑤2 𝑧𝐿𝑝𝑙 2𝑟2

𝑤2 𝑧exp 𝑖𝑙𝜙

exp𝑖𝑘0𝑟

2𝑧

2(𝑧2+𝑧𝑅2)

exp −𝑖 2𝑝 + 𝑙 + 1 tan−1𝑧

𝑧𝑅

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Magnitude

Phase

LG01 LG02 LG11 • Optical vortex carries 𝑙ℏ of orbital angular momentum per photon other than spin angular moment which originate from right or left circular polarization.

L. Allen, et. al. PRA 45 8185-8189 (1992).

Higher harmonics from helical undulators

𝐴 𝛾𝜃, 𝜙 = Τ𝐴𝑥 − 𝑖𝐴𝑦 2

= 2 exp 𝑖 𝑛 − 1 𝜙 𝛾𝜃 −𝑛𝐾

𝑋𝐽𝑛 𝑋 − 𝐾𝐽𝑛

′ (𝑋)

Shigemi Sasaki and Ian McNulty

PRL 100, 124801 (2008)

• Higher harmonics from helical undulators become optical vortex.

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𝑑2𝐼

𝑑𝜔𝑑Ω=𝑒2𝛾2𝑛2𝜉2

4𝜋𝜖0𝑐𝐴𝑥

2 + 𝐴𝑦2𝐿

𝑁Δ𝜔

𝜔

Intensity distribution equation for APPLE undulator

First Experimental Demonstration

J.Bahrdt, et. al. PRL 111, 034801 (2013).

Interference pattern from tandem undulator at photon energies of 99 eVBESSY II Storage ring E = 917 MeV

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7

Experiment at UVSOR-III storage-ring

E : 500 MeVε : 8 nmrad

Diffraction limited Wavelength ~100 nm

Experiment at UVSOR-III

Circular polarizationFundamental 710 nm2nd 355 nm

CCD camera

Bandpass filter355 nm ±2.2 nm FWHM

Linear polarizationFundamental 355 nm

Interference pattern of linear and helical

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Linear + Left Cir Linear + Right Cir

Simulation results by SRW

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https://github.com/ochubar/SRW

Experiment at UVSOR-III

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Phase shifter

Wire gridPolarizer

CCD camera

Bandpass filter355 nm ±2.2 nm FWHM

Right Circular polarizationFundamental 710 nm2nd 355 nm

Left circular polarizationFundamental 355 nm

1st right circular and 2nd harmonics left circular mode

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Without polarizer With polarizer

1st right circular and 2nd harmonics left circular mode

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0 °

1st right circular and 2nd harmonics left circular mode

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Experiment at UVSOR-III

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Wire gridPolarizer

Bandpass filter355 nm ±2.2 nm FWHM

Right Circular polarizationFundamental 710 nm2nd 355 nm

Left circular polarizationFundamental 355 nm

Phase shifter

CCD camera

Phase shifter rotates the spiral pattern

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• Bump orbit was made in between undulators by phase shifter.The orbit lengthening converted the relative phase retardation.

25.8°of relative phase retardation

Phase shifter simulation

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000 degree 090 degree90 degree

Experiment at UVSOR-III

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Phase shifter

Wire gridPolarizer

CCD camera

Bandpass filter248 nm± 1 nm FWHM

Right Circular polarizationFundamental 496 nm2nd 248 nm

Left circular polarizationFundamental 496 nm 2nd 248 nm

2nd harmonics right circular and 2nd harmonics left circular mode with polarizer

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Conclusion

• Experiment on optical vortex was performed in UVSOR-III

• We measured the interference patterns of following• Fundamental from the linear undulator and second harmonics of

right and left circularly polarized from the helical undulator.

• Fundamental from the right circularly polarized undulator and second harmonics from the left circularly polarized helical undulator.

• Second harmonics from the left circularly polarized and right

circularly polarized helical undulators.

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